Use of neural network based matched filter for fast response time in high-speed communications channels

ABSTRACT

A neural network is used within a receiver to discriminate a large set of input waveforms without using a very large set of conventional matched filters. The neural network is trained under actual line conditions as opposed to the requirement for ideal signals when using matched filters. The finite waveforms are based on digital modulation principles. A best match is made between a received waveform from the noisy channel and that of previously trained waveforms in order to extract data. Neural network based matched filter allows data be discriminated separately for each sub-carrier channel in the receiver. The neural network system allows fast processing and is suitable for high-speed data communications systems.

PRIORITY AND RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 61/837,742, filed Jun. 21, 2013, entitled “Use Of NeuralNetwork Based Matched Filter For Fast Response Time In High-SpeedCommunications Channels,” which is hereby incorporated by reference inits entirety.

FIELD OF THE INVENTION

The present invention relates to method and apparatus for improving theprocessing time of matched filters while maintaining resource efficiency(size of the resulting hardware implementation, and power consumption)for any communications system with any type of modulation scheme.

BACKGROUND OF THE INVENTION

A typical communications system can be modeled in terms of sending side200 and a receiving side 400 with a channel 300 in between them. Thesending side 200 usually consists of a data source 210 which generatesdata (bits) and a modulation system 220 which typically has a carrierwhich is modulated by the data and the output of the modulation systemis band-limited using a Transmit Band Pass Filter (TBPF) 240. The outputof the TBPF 240 is sent over a communications channel 300 to thereceiving side 400. The channel 300 corrupts the transmitted signal withnoise and any interference that might be exhibited due to the channelconditions. Also, the transmitted frequencies vary in frequency, phaseand amplitude.

At the receiving side 200, the signal received from the channel 300 ispassed through a Receive Band Pass Filter (RBPF) 410 that allows themodulated signal but limits the channel noise to the demodulator. Themodulated signal is demodulated and passed through a matched filter 500for data recovery. The impulse response of the matched filter 500 istrained with an initial signal without the channel noise for optimumwaveform generation causing it to respond only to the specifictransmitted signal on which it was trained. The demodulator outputrecovered with the band-limited channel noise is compared with theoptimum waveforms generated to accurately estimate the data transmitted.As the number of waveforms increases due to the higher speed dataoperation, the noise immunity is reduced and therefore Bit Error Rates(BER) is increased. This limits the use of conventional matched filterthat is optimized with known “expected waveforms” under no channelconditions as the data transfer rate is increased in bandwidth limitedchannel and thereby making it difficult to increase the data ratessignificantly. FIG. 1 shows a basic block diagram of a communicationssystem.

Matched filters have been used for many years in communications channelsto achieve optimized Bit Error Rate (BER) performance as a function ofEnergy per bit over Noise Density (E_(b)/N₀). When the channel carrieshigh-speed data, there is a degree of difficulty in conventional matchedfilters to characterize the channel condition in real time. One can usedelayed characterization which is even more pronounced as the datatransmission rate is significantly increased in a bandwidth limitedchannel. The noise immunity reduces to distinctly match the waveforms torecover the data at the receiver. Conventional matched filters which aretrained under no noise condition tend to have more errors on high-speeddata transmission as the noise immunity is reduced. As a result use ofconventional matched filters cause ambiguities in data recovery andcause bit error rates to increase even when modestinter-frequency-interference is present. Therefore, the Eb/NO has to beset higher for better Bit Error Rates.

An improved matched filter is desired that will characterize channelconditions in real time. An improved matched filter is needed that willincrease the predictability of data even when data transmission ratesare increased. A filter is further needed that achieves better dataaccuracy under channel noise condition when compared to conventionalmatched filters even when the noise immunity is reduced in high-speeddata transmission. Further a communication system is desired that usesan improved matched filter that reduces real estate when compared tosuch conventional matched filters implemented at a receiver.

BRIEF SUMMARY OF THE INVENTION

A communication channel having super resonance filters that correspondin number to neural network matched filters. Where 4 neural networkmatched filters and 4 super resonance filters are employed in a 12 bitsystem, the output of the neural network matched filters is 3 bits each.The neural network matched filter includes a cubic polynomial transferfunction that is employed to process input obtained from each said superresonance filter. The neural network matched filters being trained onnoisy channel data so that the filters can be trained on the actualchannel in use. The present invention reduces the need for separatechannel compensation that is usually present in conventional matchedfilter systems. The neural network matched filters are trained, oradapted, while in use. Once initial training is accomplished, gradualchanges in the channel characteristics will be accommodated bycontinuous periodic re-training of the neural network. This re-trainingfurther enhances the data recovery process as the neural network matchedfilter is adapted to the stochastically varying channel noise.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a block diagram of a single frequency conventionalcommunication system of the prior art.

FIG. 2 is a block diagram of a prior art multi-frequency communicationsystem as taught in U.S. Pat. No. 8,233,564.

FIG. 3 is a block diagram of a multi-frequency communication system ofthe current invention using a neural network based matched filter.

FIG. 4 is a block schematic diagram of the receive section for onesub-channel (uses one sub-carrier or frequency).

FIG. 5 shows architecture of one neural net based matched filter.

FIG. 6 shows a cubic polynomial approximated transfer function.

FIG. 7 shows a derivative of a cubic polynomial approximated transferfunction Derivative of Cubic Polynomial Approximated Transfer Function.

DETAILED DESCRIPTION OF THE INVENTION

In order to understand the Neural Network Based Matched Filter shown inFIG. 3 a brief description about the current state of the art isprovided below using digital compression system described in U.S. Pat.No. 8,233,564 entitled “Method And Apparatus For Increasing The ChannelCapacity Of Bandwidth Limited Communications Path”, which isincorporated by reference. The '564 system enables service providers toincrease the data rates of orders of magnitude higher than previouslysupported data rates for both wired and wireless infrastructures.Driving this evolution is the customers' increasing expectations forspeed, bandwidth and smart mobile devices to support business andconsumer applications, and entertainment available through hand-helddevices.

FIG. 2 shows the block schematic diagram of the high speed datatransmission system taught in the '564 system. The symbols in FIG. 2represent:

-   i_(j)(t) outputs of TXSRF at different closely spaced frequencies-   a_(n)(t) discrete multi-level modulation-   f_(TX) ^((n)) frequency of the LO-   f_(RX) ^((n)) frequency of the LO-   y₁(t) sum of the multi-frequency modulated signals-   y₀(t) output of the Correlator of the desired signal in the presence    of interferers

The overall '564 system uses overlapped modulation of subcarriers byindependent data stream. The combined modulated frequencies are thentransmitted over a 1 MHz channel. The data 210 of 1 Mega symbols/secondis used to generate a Pulse Amplitude Modulated (PAM) 220 signal foreach Transmit Source Resonance Frequency (TXSRF) system 230. The PAMsignal 220 is sampled and processed by the TXSRF 230 of specificsubcarrier specified by its Local Oscillator used. It produces spikewaveform, i_(i)(t) 232 with distinct amplitude using a regenerativeprocess for each symbol. The outputs of all TXSRFs 230 are combined andpassed through a Transmit Band Pass Filter (TXBPF) 240 of 1 MHz toproduce y₁(t) 242 with all modulated subcarriers within the pass-band.

The subcarriers are chosen between 250 KHz to 750 KHz. Each subcarrieris modulated by 1 Mega Symbols/second symbol rate with each symbol carryeither 1 bit or 2 bits based on the overall data rate chosen for anapplication. Since the subcarriers are not orthogonal, the combinedmodulated subcarriers introduce the inter-frequency-interference. Thisallows the 1 MHz bandwidth after the TXBPF 240 to preserve the phase andamplitude characteristics distinctly for each subcarrier.

The transmit signal is transmitted over an Additive White Gaussian Noice(AWGN) channel. This signal received at the channel is passed through a1 MHz Receive Band Pass Filter (RXBPF) 410 before it is sent to ReceiveSuper Resonance Filters (RXSRFs) 420 operating at different LocalOscillator (LO) subcarriers. The RXSRF circuitry is used for recoveringthe data from the combined band-limited TXSRF signal by a similarregenerative process as that of the TXSRF centered around each LO tosuppress the inter-frequency-interference and any other externalinterference. The output of each RXSRF is then processed at conventionalmatched filters 500 as shown in FIG. 2.

The difference between ordinary communication systems such as that shownin FIG. 1 and the '564 system shown in FIG. 2 is that the '564 systemhas SRF's. Ordinary communication systems don't have SRF's so there theRXFBF 410 would go out directly to matched filters 500. The number ofmatched filters equals the number of symbols, M, which is controlled bythe number of bits, k. Thus, where M=2^(k), a 12-bit system wouldprovide 2¹² or 4096 symbols and require the same number of matchedfilters 500. So in an ordinary communication system 100 where there are12 bits, the RXFBF 410 would connect to 4096 matched filters 500.However, in the system 1000 in FIG. 2 a lot less matched filters 500would need to be used when compared to the ordinary system. Thus, in a12 bit system employed in the system 1000, the 4096 symbols would mean4096 matched filters are required but as there are four RXSRF's eachRXSRF would handle a quarter of the matched filters or a set of 1024matched filters 500. Therefore, the neural network implementationreduces the real estate in hardware.

Looking now to FIG. 3, a neural network based matched filter 600 of thepresent invention is shown employed with a communications channel system1100. The overall design of system 1100 is similar to the system 1000 inFIG. 2 and includes a Modulation and Transmit Source ResonanceFrequencies 230, 420, channel 300, receiver and data recovery processesand a neural network based matched filter 600.

Modulation and Transmit Source Resonance Frequencies

The system 1100 is configured to transmit 4 to 8 subcarriersfrequencies. These subcarriers are each capable of modulation by 1, 2 or3 bits, yielding a system that handles 4 to 24 bits of data per symbolperiod of 1 μs. The system 1100 will also permit complex, I/Qmodulation, which doubles the capacity of the system to near the Shannonlimit. Table 1 illustrates various operating modes of bits persubcarrier frequency.

Subcarrier Bits per frequency Frequency 1 2 3 4 4 8 12 6 6 12 18 8 8 1624

In Table 1, the subcarrier frequencies under in the 1 bit per frequencycolumn are preferred from a bit error rate (BER) perspective, thesubcarrier frequencies in the 2 bits per frequency column have beentested in simulation and the subcarrier frequencies in the 3 bits perfrequency column are shown to be possible configurations. As mentionedabove, the current invention provides examples of a 12 bitimplementation which is provided by 3 bits by 4 subcarrier frequenciesor 2 bits by 4 subcarrier frequencies. Such examples should not beviewed as limiting. The subcarrier frequencies here are not orthogonalbut are rather closely spaced on the order of tens of kilohertz. Theoperation of the Transmit SRF 230 is to convert the modulated subcarriersignals into a set of 4 to 8 nearly-orthogonal signals. A criticalproperty of this approach is that these signals are added together intoone signal and filtered for output on a suitable band-limited channel.In actual implementation of the transmit section, the Transmit SRF 230does not have to run continuously. The output of the Transmit SRF 230can be tabled, and transmit symbols built from a lookup table. Thisreduces the transmit-side circuitry to a simple minimum.

Channel Requirements:

Spectral efficiency is an index computed by dividing the data rate bythe channel bandwidth. E.g., (24 Mb/s)/1 MHz=24 bits/second/Hz. If thesystem 1100 carries data in 6 closely spaced frequencies uses a channelbandwidth of 1 MHz to achieve a spectral efficiency of up to 24bits/second/Hz. When the channel is 1 MHz, the values in the table aboveare the spectral efficiency of the system.

Receiver and Data Recovery process:

The receiver 410 obtains the 1 MHz band-limited signal from the channel300. This signal is filtered and up-sampled to the receive SRF 420sampling rate, nominally 128 Mega samples/second (MS/s). The up-sampledsignal is applied to a Receiver SRF 420, a circuit similar to theTransmit SRF 230. Unlike the Transmit SRF 230, each Receiver SRF 420runs continuously and produces thirty-two outputs. These outputs areapplied to a neural network for discrimination. In anotherimplementation, a 64 MS/s signal is input and the RXSRF 420 produces 8words per microsecond. In either example the neural network matchedfilter 600 will have 1, 2, or 3 bits out. As likely evident above, theselection of MS/s and words per microsecond are engineering choices madeduring the design phase to accommodate requirements of a specificapplication and the available channel characteristics.

Neural Network Based Matched Filter 600

The neural network determines the most likely input data in the presenceof noise at the receiver as it receives the output from each RXSRF.Neural network based matched filter 600 is trained by sending known dataover each frequency. The frequencies are closely spaced and the combinedsignal is band-limited. In contrast, as described above, theconventional matched filter approach requires a significant number ofmatched filters to extract the data from each of the frequencies. Evenin system 1100 of FIG. 3, though the use of RXSRF (Receive SRF) 420minimizes the inter-frequency-interference, the impulse response foreach of the matched filter 500 needs to be determined with the trainingdata.

In the current invention with the neural network approach, the number ofneural networks 600 required is significantly reduced over the number ofmatched filters otherwise required. As mentioned above, in a 12-bitsystem there are 4096 symbols and thus 4096 matched filters. If system1100 is a 12-bit system having four subcarrier frequencies, four RXSRFsthen, according to Table 1, the number of neural network matched filters600 required would be four with each neural network matched filter 600putting out 3 bits per frequency. This is true as the number of neuralnetworks will equal the number of subcarrier frequencies and the numberof RXSRFs. So if system 1100 is a 12-bit system having six subcarrierfrequencies, six RXSRFs, and six neural network matched filters 600 eachneural network matched filter 600 would output 2 bits per frequency

Also, the training for extracting the data from each of the RXSRF 420can be extracted to generate a best estimate of the data. The bestestimate is stored for all possible combinations of data. When theactual data is transmitted, the output of the neural network is matchedto the best estimate of the original data applied to the system. Theoutput of the neural network trained matched filter is the receiver'sbest estimate of the original data applied to the system.

Since the neural network based matched filter derives the output fortransmitted data under the presence of channel noise, it is moreaccurate than conventional matched filters for recovering the actualdata lower at a lower Eb/N0. The amount of channel noise used duringtraining will be set based on the actual SNR of the channel, allowingthe overall system using a neural network based matched filter toperform better. In addition to the improved system reducing the numberof neural networks, the overall real estate in the hardware and powerconsumed by the hardware can be reduced.

FIG. 4 illustrates a block diagram of the neural network based matchedfilter 600 for a single subcarrier frequency that discriminates signalsfor data recovery. An incoming RF signal, or an incoming baseband signalis re-sampled to the desired Receive SRF sampling frequency. Thesampling rate can be pre-set to any value and the results are notimpacted. In one example, if the input to the system is RF, it isdemodulated to baseband, filtered, and re-sampled to 128 MS/s (Millionsamples per second). If the input to the system is baseband, it isfiltered and up-sampled to 128 MS/s. It is the 128 MS/s representationof the input signal which is applied to each Receive SRF.

For every subcarrier frequency in the input, there is one Receive SRF420 and one neural network based matched filter 600. A closer look atthe architecture of the Neural Net Based Matched Filter 600 is shown inFIG. 5. The neural network based matched filter 600 uses a two layerfitting network, one hidden layer 610 and one output layer 650. Thehidden layer 610 is shown in FIG. 5 to have 24 nodes but may have moreor less in other embodiments.

In one example, the output of the Receive SRF 420 consists of 32 fixedpoint words each symbol time, or 1 μs. This vector of 32 words isapplied to the hidden layer 610 of the neural network 660. The 32words/μs are multiplied by a set of 32 weights, W, 620 at each of the 24nodes. This is an ordinary dot product between the 32 input words andthe 32 weights, which is carried out on each of the 24 nodes. After thedot product, a 32 word bias vector is added to the dot product. As aresult of processing at the hidden layer 610 the 32 words are broughtdown to 24 words which are then pushed through the transfer function F,640. The transfer function F 640 employed herein is described below inrelation to equation 2.

The 24 numbers as the output of the hidden layer 610 is then processedby the output layer 650 in a similar process as in the hidden layer 610but without processing at a transfer layer in the output layer 650. Theresult at the output layer 650 is a whole number that can be convertedfrom a decimal to a binary number. In the present example 3 bits areproduced so the whole number resulting from the output layer 650 ismapped to a 3-bit binary number. In another embodiment, the input fromthe SRF 420 can be 8 words which pass into 8 nodes in the hidden layer610 resulting in a total of 64 input weights which is far less than theweights employed in the previous example with 32 input and 24 weights.

The number of neural network based matched filters 600 implemented for asystem 1100 that operates with 4 modulated and shaped frequenciescarrying a total of 12 bits of data within 1 MHz produces a spectralefficiency of 12 bits/second/Hz. For this system, the number of neuralnetworks used is 4. Whereas, with conventional matched filter approachwould require a total of 2¹² (or 4096) matched filters to recover thedata. It increases the real estate in hardware by orders of magnitudeand the processing time in parallel operation is significantly high.Accordingly, use of neural network based matched filters 600 show asignificantly reduced number of matched filters by orders of magnitudewhen compared to the number of conventional matched filters. In thesystem 1100 where 12 bits are used the number of neural network basedmatched filters are reduced to 4 compared to 4096 conventional matchedfilters used in a 12 bit system 100.

After the dot product and bias addition, each resulting scalar isapplied to a transfer function F, 640. In most function-fitting neuralnetworks, the typical transfer function F is a symmetric sigmoidtransfer function (“tansig”) shown in equation (1) below.

$\begin{matrix}{y = {\frac{2}{1 + ^{{- 2}x}} - 1}} & (1)\end{matrix}$

The transfer function 640 is applied to each of the 24 scalars from thedot product and addition, resulting in an output of a 24 word vectorpassed to the output layer 650.

Tansig transfer functions are difficult to synthesize in hardware usingFPGAs such as Xilinx Vertex 6 Field Programmable Gate Arrays which maybe used in the current invention. The difficulty is attributed to theneed to calculate an exponential and perform a division. In the currentinvention the tansig transfer function is replaced with a cubicpolynomial designed to approximate a tan sigmoid curve. This transferfunction, F, 640 consists of a process to limit the input range to ±1,followed by a cubic polynomial shown in the formulas in equation 2below. This novel implementation of the cubic polynomial designedtransfer function, F, to approximate the tan sigmoid curve is truncatedto manage the input within the range of ±1. The truncated sigmoid curveis easier to implement using conventional addition and multiplicationcompared to the tan sigmoid which requires computation of “exponential”and “division” operation, as stated above.

The resulting transfer function F 640 based on equation (2) is shown inFIGS. 6 and 7 for u and y respectively. FIG. 6 shows a curve that is anapproximation of the tansig while FIG. 7 shows the first derivativethereof which is well-behaved outside −1 to 1 and zero between −1 and 1.The use of equation 2 in the transfer function, F makes it practical foruse in the FPGA.

$\begin{matrix}{{u = {\max ( {{- 1},{\min ( {1,\frac{u}{2}} )}} )}}{y = {( \frac{u}{2} )*( {3 - u^{2}} )}}} & (2)\end{matrix}$

The output layer 650 computes a single dot product between the output ofthe hidden layer 610 and a 24 element weight vector. A scalar bias isapplied. The resulting scalar is then passed through an output layertransfer function 680. In this system the output layer transfer function680 is trivial: y=x. Since dot product is purely arithmetic, it reducesthe complexity in using truncated cubic function compared to usingtansig function. This will reduce the number of gates (or real estate)in the FPGA.

The neural network based matched filter 600 generates an output value inthe range of −1.5<y<1.5. Depending on the number of input bitstransmitted over a subcarrier channel in the transmitter, thresholds areset up so that a comparator chooses the closest noiseless data point,and assigns a binary value accordingly. For example, if only one bit istransmitted per subcarrier, a simple sign operation selects a 0 or 1output. For two bits, the ideal values are [−1, −⅓, ⅓, 1]. These valuescorrespond to binary values [00, 01, 10, 11]. The neural network cancompute this output either in the fixed point case, in which the neuralnetwork is followed by a comparator; or it can incorporate thecomparator. In contrast, the '564 system design uses a separatecomparator to obtain the 1, 2 or 3 bits of output per subcarrierchannel.

The current invention uses the neural network as a matched filter undera given channel noise condition. The neural network based matched filter600 thus increases the predictability of the data even when the datatransmission rate is increased. The neural network based matched filter600 also significantly increases the accuracy of the data recovery whencompared to conventional matched filters 500 used in communications.

A conventional matched filter implementation requires training on anoiseless version of the channel to be used. The penalty of using neuralnetworks 600 is that it not only requires training initially on a givenchannel with noise, but also requires periodic retraining to adapt theneural network for channel noise variation. However, since the trainingis on a noisy known signal, many problems associated with theconventional matched filter are avoided. This trade-off between trainingof neural network for channel conditions and better accuracy of datarecovery does not increase the circuit complexity significantly even forhigh-speed data transmission applications. Therefore achieving betterdata accuracy under channel noise condition is achievable even when thenoise immunity is reduced in high-speed data transmission whereas,conventional matched filters 500 which tend to be trained under no noisecondition tend to have more errors on high-speed data transmission asthe noise immunity is reduced. The implementation of neural networkbased matched filter 600 is particularly useful in wireless channelswhere multi-path fading impairments and Doppler effects exist.

Neural Network Training

A set of training data consists of two components. The target data is along (4096 symbol) sequence of data inputs to the transmitter. This isconsidered “truth” or baseline data. The transmitter modulates thisstream, and sends it to the receiver, where it is eventually applied tothe input of the neural networks. Because the input data to thetransmitter is known, the original target data is used in the trainingprocess as the target of an optimization process. TheLevenberg-Marquardt algorithm, or a similar algorithm such as conjugategradient back propagation, is used to find a set of weights for each ofthe neural networks so that the mean square error between the idealtarget output and the actual output during training is minimized.

This training is performed on a newly-initialized system, and isrepeated whenever there is sufficient change in the channel to warrantretraining, as measured by an increasing bit error rate. However, duringnormal operation, channel changes will occur continuously, butrelatively slowly. Therefore, a periodic set of training data may besent to incrementally adjust the neural net weights as needed.

While the present invention has been described in conjunction withspecific embodiments, those of normal skill in the art will appreciatethe modifications and variations can be made without departing from thescope and the spirit of the present invention. Such modifications andvariations are envisioned to be within the scope of the appended claims.

1. A communication channel transmitting a number of subcarrierfrequencies comprising: super resonance filters; and neural networkbased matched filters, wherein each the super resonance filters and eachthe neural network based matched filters equal in number to the numberof said subcarrier frequencies.
 2. The channel of claim 1, wherein at a1-bit output at each said neural network matched filter said subcarrierfrequencies equals in number to a number of bits for the channel.
 3. Thechannel of claim 1, wherein at a 2-bit output at each said neuralnetwork matched filter said subcarrier frequencies is half in number toa number of bits for the channel.
 4. The channel of claim 1, wherein ata 3-bit output at each said neural network matched filter saidsubcarrier frequencies is one-third in number to a number of bits forthe channel.
 5. The channel of claim 1, wherein said neural networkmatched filter includes a cubic polynomial transfer function.
 6. Amethod of reducing hardware complexity and speed of processing datarecovery in a communication system comprising: training neural networkmatched filters, on noisy channel data of said system; receiving anumber of subcarrier frequencies in said system; providing a number ofsuper resonance filters, wherein said number of super resonance filtersequals in number to said number of subcarrier frequencies and saidneural network matched filters.
 7. The method of claim 6, wherein aftersaid training of said neural network, said neural network is adaptedwhile in use.
 8. A neural network matched filter having a cubicpolynomial transfer function.